Calculate the median from the following data:


Height - (in cm)



135 - 140



140 - 145



145 - 150



150 - 155



155 - 160



160 - 165



165 - 170



170 - 175



No. of boys



6



10



18



22



20



15



6



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To find median, Assume

Σfi = N = Sum of frequencies,


h = length of median class,


l = lower boundary of the median class,


f = frequency of median class


and Cf = cumulative frequency


Lets form a table.


HEIGHT(cm)



NUMBER OF BOYS(fi)



Cf



135 - 140



6



6



140 - 145



10



6 + 10 = 16



145 - 150



18



16 + 18 = 34



150 - 155



22



34 + 22 = 56



155 - 160



20



56 + 20 = 76



160 - 165



15



76 + 15 = 91



165 - 170



6



91 + 6 = 97



170 - 175



3



97 + 3 = 100



TOTAL



100




So, N = 100


N/2 = 100/2 = 50


The cumulative frequency just greater than (N/2 = ) 50 is 56, so the corresponding median class is 150 - 155 and accordingly we get Cf = 34(cumulative frequency before the median class).


Now, since median class is 150 - 155.


l = 150, h = 5, f = 22, N/2 = 50 and Cf = 34


Median is given by,




= 150 + 3.636


= 153.64


Thus, median is 153.64 cm.


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